Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2511.00150

Simulated outperforms quantum reverse annealing in mean-field models

Christopher L. Baldwin

Published Oct 31, 2025• 0 citations
arXivHTMLPDF

Abstract

Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase transitions. Here we interpret the performance of ARA through its effects on the free energy landscape, and use the intuition gained to introduce a classical analogue to ARA termed ``simulated reverse annealing'' (SRA). This makes it more difficult to claim that ARA provides a quantum advantage in solving a given problem, as not only must ARA succeed but the corresponding SRA must fail. As a solvable example, we analyze how both protocols behave in the infinite-range (non-disordered) $p$-spin model. Through both the thermodynamic phase diagrams and explicit dynamical behavior, we establish that the quantum algorithm has no advantage over its classical counterpart: SRA succeeds not only in every case where ARA does but even in a narrow range of parameters where ARA fails.

DOI
10.48550/arxiv.2511.00150

Related papers

Adiabatic reverse annealing is robust to low-temperature decoherence

An Le, Christopher L. Baldwin

Adiabatic reverse annealing (ARA) is an improvement to conventional quantum annealing (QA) that uses an initial guess at the desired ground state to circumvent problematic phase transitions. Despite encouraging results in the closed-system setting, Ref. [1] has suggested on the basis of numerical simulations that ARA may lose its advantage in the presence of decoherence. Here, we revisit this problem from a more analytical perspective. Using the $p$-spin model as a solvable example, together with the adiabatic master equation to describe the effects of the environment (valid at weak coupling), we show that ARA can in fact succeed in open systems but that the temperature of the environment plays a key role. We first demonstrate that, in the adiabatic limit, the system will follow the instantaneous equilibrium state as long as the protocol does not pass through any (finite-temperature) phase transitions. Given this, there are two distinct mechanisms by which ARA can break down at high temperature: either there are no paths that avoid transitions, or the equilibrium state itself is disordered. When the temperature is sufficiently low that neither of these occur, then ARA succeeds. Remarkably, there are even situations in which the environment benefits ARA: we find parameter values for which no transition-avoiding paths exist at zero temperature but such paths appear at non-zero temperature.

quant-pharXiv:2511.16735•Nov 24, 2025•0 citations

Standard quantum annealing outperforms adiabatic reverse annealing with decoherence

Gianluca Passarelli, Ka-Wa Yip, Daniel A. Lidar +1 more

We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy ARA is unlikely to experimentally outperform standard ``forward'' quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings.

arXiv:2201.11997•Physical Review A•Mar 18, 2022•14 citations

Dynamics of reverse annealing for the fully connected p-spin model

悠 山城, Yu Yamashiro, 秀稔 西森 +2 more

Reverse annealing is a relatively new variant of quantum annealing in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the initial state for a given optimization problem.We numerically study the unitary quantum dynamics of reverse annealing for the mean-field-type p-spin model and show that the results are consistent with the predictions of equilibrium statistical mechanics.In particular, we corroborate the equilibrium analysis prediction that reverse annealing provides an exponential speedup over conventional quantum annealing in terms of solving the p-spin model.This lends support to the expectation that equilibrium analyses are effective at revealing essential aspects of the dynamics of quantum annealing.We also compare the results of quantum dynamics with the corresponding classical dynamics to reveal their similarities and differences.We distinguish between two reverse annealing protocols we call adiabatic and iterated reverse annealing.We further show that iterated reverse annealing, as has been realized in the D-Wave device, is ineffective in the case of the p-spin model but note that a recently introduced protocol ("h-gain"), which implements adiabatic reverse annealing, may lead to improved performance.

•Nov 1, 2019•0 citations

Reverse annealing for the fully connected p -spin model

Masaki Ohkuwa, Hidetoshi Nishimori, Daniel A. Lidar

Reverse annealing is a variant of quantum annealing that starts from a given classical configuration of spins (qubits). In contrast to the conventional formulation, where one starts from a uniform superposition of all possible states (classical configurations), quantum fluctuations are first increased and only then decreased. One then reads out the state as a proposed solution to the given combinatorial optimization problem. We formulate a mean-field theory of reverse annealing using the fully connected ferromagnetic $p$-spin model, with and without random longitudinal fields, and analyze it in order to understand how and when reverse annealing is effective at solving this problem. We find that the difficulty arising from the existence of a first-order quantum phase transition, which leads to an exponentially long computation time in conventional quantum annealing, is circumvented in the context of this particular problem by reverse annealing if the proximity of the initial state to the (known) solution exceeds a threshold. Even when a first-order transition is unavoidable, the difficulty is mitigated due to a smaller jump in the order parameter at a first-order transition, which implies a larger rate of quantum tunneling. Reverse annealing has not been studied analytically before, and this study paves the way toward a systematic understanding of this relatively unexplored protocol in a broader context.

arXiv:1806.02542•Physical Review A•Aug 13, 2018•112 citations

Mean-Field Analysis of Sourlas Codes with Adiabatic Reverse Annealing

Shunta Arai

Abstract In this chapter, we analyze the typical performance of adiabatic reverse annealing (ARA) for Sourlas codes. Sourlas codes are representative error-correcting codes related to p-body spin-glass models and have a first-order phase transition for $$p>2$$ p > 2 , which degrades the estimation performance. In the ARA formulation, we introduce the initial Hamiltonian which incorporates the prior information of the solution into a vanilla quantum annealing (QA) formulation. The ground state of the initial Hamiltonian represents the initial candidate solution. To avoid the first-order phase transition, we apply ARA to Sourlas codes. We evaluate the typical ARA performance for Sourlas codes using the replica method. We show that ARA can avoid the first-order phase transition if we prepare for the proper initial candidate solution.

Springer eBooks•Oct 19, 2021•0 citations

Extending the computational reach of Quantum Annealing using Reverse Annealing

Lucas Joshua Menger, Thomas Lippert, Manpreet Singh Jattana

Quantum annealing is a promising heuristic for combinatorial optimization, but on current hardware its performance degrades for larger and more complex problems due to noise and small energy gaps. Reverse annealing has been proposed as a refinement strategy, yet it remains unclear when it provides systematic advantages over standard forward annealing or simply increasing annealing time. We find that combining forward and reverse annealing consistently improves solution quality and efficiency across multiple problem classes. The benefits of reverse annealing increase with problem complexity and are strongest in regimes where forward annealing is increasingly limited. Moreover, reverse annealing yields larger efficiency gains than simply extending forward annealing times. We establish these results through a systematic experimental study on a D-Wave Advantage system, benchmarking reverse annealing across Max-Cut, Number Partitioning, and sparse clustering problems while varying reverse distance, pause duration, and annealing time. We identify a narrow optimal regime for reverse annealing parameters linked to the location of freeze-out points and energy-level crossings in the annealing schedule. These findings demonstrate that reverse annealing is most valuable for large, high-complexity optimization problems and is likely to gain importance as quantum annealing hardware scales toward more realistic applications.

quant-pharXiv:2607.02146•EPJ Quantum Technology•Jul 3, 2026•0 citations
Adiabatic reverse annealing (ARA) has been proposed as an improvement to conventional quantum annealing for solving optimization problems, in which one takes advantage of an initial guess at the solution to suppress problematic phase transitions. Here we interpret the performance of ARA through its effects on the free energy landscape, and use the intuition gained to introduce a classical analogue to ARA termed ``simulated reverse annealing'' (SRA). This makes it more difficult to claim that ARA provides a quantum advantage in solving a given problem, as not only must ARA succeed but the corresponding SRA must fail. As a solvable example, we analyze how both protocols behave in the infinite-range (non-disordered) ppp-spin model. Through both the thermodynamic phase diagrams and explicit dynamical behavior, we establish that the quantum algorithm has no advantage over its classical counterpart: SRA succeeds not only in every case where ARA does but even in a narrow range of parameters where ARA fails.
Adiabatic reverse annealing (ARA) is an improvement to conventional quantum annealing (QA) that uses an initial guess at the desired ground state to circumvent problematic phase transitions. Despite encouraging results in the closed-system setting, Ref. [1] has suggested on the basis of numerical simulations that ARA may lose its advantage in the presence of decoherence. Here, we revisit this problem from a more analytical perspective. Using the ppp-spin model as a solvable example, together with the adiabatic master equation to describe the effects of the environment (valid at weak coupling), we show that ARA can in fact succeed in open systems but that the temperature of the environment plays a key role. We first demonstrate that, in the adiabatic limit, the system will follow the instantaneous equilibrium state as long as the protocol does not pass through any (finite-temperature) phase transitions. Given this, there are two distinct mechanisms by which ARA can break down at high temperature: either there are no paths that avoid transitions, or the equilibrium state itself is disordered. When the temperature is sufficiently low that neither of these occur, then ARA succeeds. Remarkably, there are even situations in which the environment benefits ARA: we find parameter values for which no transition-avoiding paths exist at zero temperature but such paths appear at non-zero temperature.
We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic ppp-spin model with p=3p=3p=3 under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy ARA is unlikely to experimentally outperform standard ``forward'' quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings.
Reverse annealing is a relatively new variant of quantum annealing in which one starts from a classical state and increases and then decreases the amplitude of the transverse field, in the hope of finding a better classical state than the initial state for a given optimization problem.We numerically study the unitary quantum dynamics of reverse annealing for the mean-field-type p-spin model and show that the results are consistent with the predictions of equilibrium statistical mechanics.In particular, we corroborate the equilibrium analysis prediction that reverse annealing provides an exponential speedup over conventional quantum annealing in terms of solving the p-spin model.This lends support to the expectation that equilibrium analyses are effective at revealing essential aspects of the dynamics of quantum annealing.We also compare the results of quantum dynamics with the corresponding classical dynamics to reveal their similarities and differences.We distinguish between two reverse annealing protocols we call adiabatic and iterated reverse annealing.We further show that iterated reverse annealing, as has been realized in the D-Wave device, is ineffective in the case of the p-spin model but note that a recently introduced protocol ("h-gain"), which implements adiabatic reverse annealing, may lead to improved performance.
Reverse annealing is a variant of quantum annealing that starts from a given classical configuration of spins (qubits). In contrast to the conventional formulation, where one starts from a uniform superposition of all possible states (classical configurations), quantum fluctuations are first increased and only then decreased. One then reads out the state as a proposed solution to the given combinatorial optimization problem. We formulate a mean-field theory of reverse annealing using the fully connected ferromagnetic ppp-spin model, with and without random longitudinal fields, and analyze it in order to understand how and when reverse annealing is effective at solving this problem. We find that the difficulty arising from the existence of a first-order quantum phase transition, which leads to an exponentially long computation time in conventional quantum annealing, is circumvented in the context of this particular problem by reverse annealing if the proximity of the initial state to the (known) solution exceeds a threshold. Even when a first-order transition is unavoidable, the difficulty is mitigated due to a smaller jump in the order parameter at a first-order transition, which implies a larger rate of quantum tunneling. Reverse annealing has not been studied analytically before, and this study paves the way toward a systematic understanding of this relatively unexplored protocol in a broader context.
Abstract In this chapter, we analyze the typical performance of adiabatic reverse annealing (ARA) for Sourlas codes. Sourlas codes are representative error-correcting codes related to p-body spin-glass models and have a first-order phase transition for p>2p>2p>2 p > 2 , which degrades the estimation performance. In the ARA formulation, we introduce the initial Hamiltonian which incorporates the prior information of the solution into a vanilla quantum annealing (QA) formulation. The ground state of the initial Hamiltonian represents the initial candidate solution. To avoid the first-order phase transition, we apply ARA to Sourlas codes. We evaluate the typical ARA performance for Sourlas codes using the replica method. We show that ARA can avoid the first-order phase transition if we prepare for the proper initial candidate solution.
Quantum annealing is a promising heuristic for combinatorial optimization, but on current hardware its performance degrades for larger and more complex problems due to noise and small energy gaps. Reverse annealing has been proposed as a refinement strategy, yet it remains unclear when it provides systematic advantages over standard forward annealing or simply increasing annealing time. We find that combining forward and reverse annealing consistently improves solution quality and efficiency across multiple problem classes. The benefits of reverse annealing increase with problem complexity and are strongest in regimes where forward annealing is increasingly limited. Moreover, reverse annealing yields larger efficiency gains than simply extending forward annealing times. We establish these results through a systematic experimental study on a D-Wave Advantage system, benchmarking reverse annealing across Max-Cut, Number Partitioning, and sparse clustering problems while varying reverse distance, pause duration, and annealing time. We identify a narrow optimal regime for reverse annealing parameters linked to the location of freeze-out points and energy-level crossings in the annealing schedule. These findings demonstrate that reverse annealing is most valuable for large, high-complexity optimization problems and is likely to gain importance as quantum annealing hardware scales toward more realistic applications.